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Approximation of lebesgue integrals by Riemann sums and lattice points in domains with fractal boundary

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Abstract

Sets thrown at random in space contain, on average, a number of integer points equal to the measure of these sets. We determine the mean square error in the estimate of this number when the sets are homothetic to a domain with fractal boundary. This is related to the problem of approximating Lebesgue integrals by random Riemann sums.

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  1. Dipartimento di Matematica, Universitá degli studi di Milano, via C. Saldini 50, 20133, Milano, Italy

    Leonardo Colzani

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  1. Leonardo Colzani
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Colzani, L. Approximation of lebesgue integrals by Riemann sums and lattice points in domains with fractal boundary. Monatshefte für Mathematik 123, 299–308 (1997). https://doi.org/10.1007/BF01326765

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  • DOI: https://doi.org/10.1007/BF01326765

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